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Research Article | Open Access

Sequential fractional order Neutral functional Integro differential equations on time scales with Caputo fractional operator over Banach spaces

Ahmed Morsy1( ), Kottakkaran Sooppy Nisar1, Chokkalingam Ravichandran2, Chandran Anusha2
Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
Department of Mathematics, Kongunadu Arts and Science College (Autonomous), Coimbatore 641029, Tamil Nadu, India
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Abstract

In this work, we scrutinize the existence and uniqueness of the solution to the Integro differential equations for the Caputo fractional derivative on the time scale. We derive the solution of the neutral fractional differential equations along the finite delay conditions. The fixed point theory is demonstrated, and the solution depends upon the fixed point theorems: Banach contraction principle, nonlinear alternative for Leray-Schauder type, and Krasnoselskii fixed point theorem.

Keywords

Neutral differential equationsfixed pointCaputo fractional derivativetime scalesSemigroup theorydelay differential equations
CLC number: 34K40, 34K42

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 5934-5949
DOI: 10.3934/math.2023299

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Cite this article:
Morsy A, Nisar KS, Ravichandran C, et al. Sequential fractional order Neutral functional Integro differential equations on time scales with Caputo fractional operator over Banach spaces. AIMS Mathematics, 2023, 8(3): 5934-5949. https://doi.org/10.3934/math.2023299

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Received: 05 November 2022
Revised: 08 December 2022
Accepted: 19 December 2022
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)